Tangi Migot

Tangi Migot

Computational Scientist

Partially differentiable projects

1 minute read

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I am starting a new year in Montreal and one of the main projects for this year is to move forward in finalizing an ecosystem for optimization problems with partial differential equations in the constraints. The ecosystem is hosted under the JuliaSmoothOptimizers umbrella and contains:

As usual modeling packages are fun, but not more than new solvers! I am focusing on two packages:

  • Fletcher’s penalty method. This method is matrix-free, which would be just perfect for huge large-scale structured problems such as PDE-constrained problems. The cherry on top of the cake is that this package uses Stopping.
  • DCISolver. This package uses a matrix-free feasibility process, but the tangent step still relies on an SQD matrix factorization using HSL or LDLFactorizations. Still, it is showing great performance even on large problems. I wrote a tutorial on jso-docs.github.io showing a comparison with Ipopt on a distributed Poisson control problem with Dirichlet boundary conditions (Spoiler alert: DCI is doing great). You can also play with a similar example on mybinder.org via the package’s documentation.

You can check the talk I gave at IVADO last October, on youtube.

The whole ecosystem is already in advanced testing and being used in my teaching at Polytechnique Montreal.

Upcoming

  • Upgrade of PDENLPModels to Gridap 0.17 (which shows great performance improvements last JuliaCon New tools to solve PDEs in Julia with Gridap.jl).
  • As usual, more problems and applications for PDEOptimizationProblems :).
  • DCISolver is under review in the Journal of Open Source Software. The whole review process was pretty fun (for once) and helped improve the package’s documentation. Hoping for the good news soon.
  • Why does FPS use Stopping?

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Presenting at JuMP-dev 2024 and Publishing in JuliaCon 2023 Proceedings

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I’m thrilled to share two major milestones in my recent work within the Julia ecosystem. First, I presented the latest developments in optimization solvers at JuMP-dev 2024, and second, my paper on JSOSuite.jl was accepted in The Proceedings of the JuliaCon Conferences.

These two achievements highlight both the ongoing evolution of JuliaSmoothOptimizers (JSO) and its growing impact on large-scale nonlinear optimization problems.

JuMP-dev 2024: Advancing Nonlinear Optimization with JuliaSmoothOptimizers

This year’s JuMP-dev workshop, held independently from JuliaCon for the first time in Montreal, offered a focused platform for deep dives into JuMP and its surrounding tools. In my presentation, I discussed the latest progress within the JuliaSmoothOptimizers (JSO) ecosystem, my slides and the replay.

At the core of my talk was an introduction to new solvers and packages like AdaptiveRegularization.jl, which address the unique challenges of large-scale optimization problems with Adaptive Regularization with Cubics. I emphasized the following key innovations:

  • Automatic Differentiation (AD) support and integration with JuMP for easier problem modeling.
  • Memory pre-allocation for in-place solvers, reducing runtime overhead.
  • Support for multi-precision solvers and GPU-based computations, essential for modern large-scale applications.
  • The value of factorization-free solvers, which excel in tackling large, complex problems, such as those in discretized PDE-constrained optimization.

For newcomers to JSO, JSOSuite.jl serves as a critical entry point, simplifying solver selection and benchmarking through automatic algorithm matching. This tool eliminates the complexity of choosing from multiple solvers by providing a user-friendly interface that adapts to the problem at hand. My talk also touched on the broader adoption and longevity of JSO, which now spans over 50 registered packages, making it one of the most comprehensive platforms for numerical optimization.

JuliaCon 2023: JSOSuite.jl – Simplifying Continuous Optimization

While JuMP-dev 2024 focused on recent developments, my publication in The Proceedings of the JuliaCon Conferences looks at the core philosophy and implementation behind JSOSuite.jl. Titled JSOSuite.jl: Solving Continuous Optimization Problems with JuliaSmoothOptimizers, the paper introduces JSOSuite.jl as a package designed to bring ease-of-use to complex optimization challenges.

JSOSuite.jl covers a range of problem types—from unconstrained to generally-constrained and least-squares problems—and eliminates the need for users to understand the intricate details of individual solvers. Instead, the package conducts a preliminary analysis of the problem and automatically selects the most appropriate solver, offering significant advantages to both experienced practitioners and newcomers alike.

This paper builds on the innovations within JSO, reinforcing its versatility and ease of use across various fields and applications. The package is a natural fit for researchers who need efficient, reliable solvers without the overhead of manually configuring them for different problem types.

Looking Forward

Both my presentation at JuMP-dev 2024 and the publication of the JSOSuite.jl paper reflect the significant strides made by the JuliaSmoothOptimizers organization over the past year. The JSO ecosystem is positioned to continue driving innovation in the field of numerical optimization.

I’m excited to see how these advancements will be applied across diverse optimization problems in the coming years and look forward to continuing this journey with the JSO community.

New Preprint on HAL: Exploring Projected Dynamical Systems in Geochemical Reactions

2 minute read

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This project holds a special place in my heart as it touches on the very applications in geochemistry that first drew me into research. Equilibrium reactions, particularly in slow processes like the water cycle in aquifers, have always fascinated me. Moreover, this paper represents an important milestone for one of the authors, Bastien, as it was part of his Ph.D. thesis. The use of projected dynamical systems, a model I am particularly fond of, adds an additional layer of personal significance to this work.